Turns out, checking it out didn't really solve the mystery. The subtitle of the site is "lolcats tagged for your convenience (also for ur lol*s)".
Um ... huh? What's a lolcat? Wikipedia tells me it's an image macro used on forums. Um ... huh? My forum experience is pretty limited, and I'd never seen anything like these out in the wild, but I Can Has Cheezburger has pages and pages of cat pictures - and dog pictures and walrus pictures - with mangled English captions. And it gets more hits every day than one of the most popular tech geek blogs out there. It gets over a quarter million hits a day. Crazy.
Slate has a hilarious slide show essay on the lolcat phenomenon, Cat Power: You Cannot Resist Lolcats. It taught me even more:
A reader pointed Dash to a San Francisco Chronicle article about MeowChat, where people maintain cat identities online and speak in a cat language that slightly overlaps with lolcat speak. (Genius detail: Some cat lovers disdain MeowChat because it implies that cats are not intelligent, evolved creatures.)
I'm sure this is exactly why those Clean Slate Internet guys want to make sure the Internet can handle future demands on it. Gotta make room for the lolcats.